GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 12 Dec 2019, 11:17

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

What is the sum of the digits of integer x, where x = 4^10* 5^13?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59712
What is the sum of the digits of integer x, where x = 4^10* 5^13?  [#permalink]

Show Tags

New post 05 Nov 2017, 02:38
1
11
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

65% (01:39) correct 35% (01:42) wrong based on 205 sessions

HideShow timer Statistics

Manager
Manager
avatar
S
Joined: 18 May 2016
Posts: 180
Location: India
GMAT 1: 710 Q48 V40
WE: Marketing (Education)
GMAT ToolKit User Reviews Badge
Re: What is the sum of the digits of integer x, where x = 4^10* 5^13?  [#permalink]

Show Tags

New post 05 Nov 2017, 02:58
3
X= 2^20*5^13
= 10^13 *2^7
= 128*10^13

Sum of digits = 11
Option B

Sent from my A0001 using GMAT Club Forum mobile app
Manager
Manager
avatar
B
Joined: 06 Aug 2017
Posts: 78
GMAT 1: 570 Q50 V18
GMAT 2: 610 Q49 V24
GMAT 3: 640 Q48 V29
Re: What is the sum of the digits of integer x, where x = 4^10* 5^13?  [#permalink]

Show Tags

New post 05 Nov 2017, 12:15
2
2
Bunuel wrote:
What is the sum of the digits of integer x, where \(x = 4^{10} * 5^{13}\)?

(A) 13

(B) 11

(C) 10

(D) 8

(E) 5


Answer is B as follows

\(x = 4^{10} * 5^{13} = 2^{20}*5^{13} = 10^{13}*2^7 = 10^{13}*128\)
Sum of the digits = 1+2+8 = 11

Hence B
Intern
Intern
avatar
Joined: 26 Jan 2017
Posts: 3
Re: What is the sum of the digits of integer x, where x = 4^10* 5^13?  [#permalink]

Show Tags

New post 07 Nov 2017, 09:05
3
Since we are looking for the sum of the digits we can simplify this problem by removing the trailing zeros (zeros at the end of the number). Trailing zeros are added to a number when multiplied by 10.

Remember 10 = 2 * 5
Thus, in our problem 4^10*5^13 or:
2^20 * 5^13

As you can see we have the pair 2*5 thirteen times. We can remove 2^13 and 5^13 and work with the rest which is 2^7 = 128

1+2+8 = 11
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2809
Re: What is the sum of the digits of integer x, where x = 4^10* 5^13?  [#permalink]

Show Tags

New post 08 Nov 2017, 17:35
4
Bunuel wrote:
What is the sum of the digits of integer x, where \(x = 4^{10} * 5^{13}\)?

(A) 13

(B) 11

(C) 10

(D) 8

(E) 5



We can simplify the given equation:

x = 4^10 x 5^13

x = 2^20 x 5^13

x = 2^7 x 2^13 x 5^13

x = 2^7 x 10^13

x = 128 x 10^13

We see that x is the number 128 followed by 13 zeros. Thus, the sum of the digits of x is 1 + 2 + 8 = 11.

Answer: B
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Intern
avatar
S
Joined: 22 May 2018
Posts: 49
Re: What is the sum of the digits of integer x, where x = 4^10* 5^13?  [#permalink]

Show Tags

New post 04 Apr 2019, 05:59
1
we can use the concept of cyclicity to find out the units digit.
units digit of 4^10 is 6 and units digit of 5^13 is 5
6+5 = 11
units digit 1.
(This method works because there is no repetition of units digit in the options.)
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8680
Location: United States (CA)
Re: What is the sum of the digits of integer x, where x = 4^10* 5^13?  [#permalink]

Show Tags

New post 07 Apr 2019, 19:04
1
Bunuel wrote:
What is the sum of the digits of integer x, where \(x = 4^{10} * 5^{13}\)?

(A) 13

(B) 11

(C) 10

(D) 8

(E) 5



We can rewrite the expression as:

2^20 x 5^13

2^7 x 2^13 x 5^13

2^7 x 10^13

128 x 10^13


This is the number 128 followed by 13 zeros, so the sum of the digits is 1 + 2 + 8 = 11 (note: the 13 zeros will not contribute anything to the sum).

Answer: B
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: What is the sum of the digits of integer x, where x = 4^10* 5^13?   [#permalink] 07 Apr 2019, 19:04
Display posts from previous: Sort by

What is the sum of the digits of integer x, where x = 4^10* 5^13?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne